Practice Questions
Concept Explanation
A number is divisible by another when division leaves zero remainder. Placement papers often test quick divisibility checks without long division.
Important Divisibility Rules
| Divisor | Rule | Example |
|---|---|---|
| 2 | Last digit is even | 846 |
| 3 | Sum of digits divisible by 3 | 582 → 15 |
| 4 | Last two digits divisible by 4 | 2,316 → 16 |
| 5 | Last digit 0 or 5 | 375 |
| 6 | Divisible by 2 and 3 | 714 |
| 8 | Last three digits divisible by 8 | 4,024 → 024 |
| 9 | Sum of digits divisible by 9 | 891 → 18 |
| 11 | Alternate digit sum difference is 0 or multiple of 11 | 1,331 → 0 |
Composite Divisors
12 needs divisibility by 3 and 4. 15 needs 3 and 5. 18 needs 2 and 9. Break composite tests into prime rules.
Rule for 7
Double the last digit and subtract from the number formed by remaining digits. Repeat until you can judge divisibility by 7.
Example: 343 → 34 − 6 = 28, and 28 ÷ 7 = 4, so 343 is divisible by 7.
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Q1 Easy
Which of the following numbers is divisible by 2?
ExplanationA number is divisible by 2 if its last digit is even (0, 2, 4, 6 or 8). The last digit of 728 is 8, so it is divisible by 2. -
Q2 Easy
Which of the following numbers is divisible by 3?
ExplanationAdd the digits of each number. For 417: 4 + 1 + 7 = 12. Since 12 is divisible by 3, 417 is divisible by 3. -
Q3 Easy
Which of the following numbers is divisible by 4?
ExplanationFor divisibility by 4, the last two digits must be divisible by 4. The last two digits of 3,124 are 24, and 24 ÷ 4 = 6. Therefore 3,124 is divisible by 4. -
Q4 Easy
Which of the following numbers is divisible by 6?
ExplanationA number is divisible by 6 if it is divisible by both 2 and 3. 246 is even, so it is divisible by 2. Sum of digits: 2 + 4 + 6 = 12, and 12 is divisible by 3. Therefore 246 is divisible by 6. -
Q5 Easy
Which digit should replace x in 52x4 so that the number is divisible by 3?
Explanation5 + 2 + x + 4 = 11 + x. For divisibility by 3, 11 + x must be a multiple of 3. If x = 1, the sum is 12, which is divisible by 3. So the digit is 1. -
Q6 Easy
Which of the following numbers is divisible by 8?
ExplanationFor divisibility by 8, the last three digits must be divisible by 8. The last three digits of 2,136 are 136, and 136 ÷ 8 = 17. Therefore 2,136 is divisible by 8. -
Q7 Easy
Which of the following numbers is divisible by 9?
ExplanationA number is divisible by 9 if the sum of its digits is divisible by 9. For 4,329: 4 + 3 + 2 + 9 = 18, and 18 is divisible by 9. The other options sum to 16, 16 and 14 — none divisible by 9.
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Q8 Easy
Which of the following numbers is divisible by 11?
ExplanationFind the difference between the sums of alternate digits. For 121: (1 + 1) − 2 = 0. Since 0 is a multiple of 11, 121 is divisible by 11. -
Q9 Easy
Which of the following numbers is divisible by both 4 and 3?
ExplanationFor 132: last two digits are 32, and 32 is divisible by 4. Sum of digits: 1 + 3 + 2 = 6, which is divisible by 3. So 132 is divisible by both 4 and 3 (and therefore by 12). -
Q10 Medium
What is the smallest digit x that can replace the blank in 47x2 to make the number divisible by 9?
ExplanationSum of digits: 4 + 7 + x + 2 = 13 + x. The next multiple of 9 after 13 is 18, so 13 + x = 18 and x = 5. Among the given options, 5 is the digit that works. -
Q11 Medium
Which of the following numbers is divisible by 7?
ExplanationApply the rule for 7: double the last digit and subtract it from the remaining number. 203 → 20 − (2 × 3) = 20 − 6 = 14. Since 14 is divisible by 7, 203 is divisible by 7. -
Q12 Medium
What is the smallest digit x that should replace the blank in 63x5 so that the number is divisible by 15?
ExplanationA number divisible by 15 must be divisible by both 3 and 5. The last digit is already 5, so it is divisible by 5. Sum of digits: 6 + 3 + x + 5 = 14 + x. 14 + x must be a multiple of 3. The smallest option that works is x = 1 (14 + 1 = 15). -
Q13 Easy
Which of the following numbers is divisible by 5?
ExplanationA number is divisible by 5 only if its last digit is 0 or 5. Among the options, 3,450 ends in 0, so it is divisible by 5. -
Q14 Medium
What is the smallest digit x that makes 84x divisible by 4?
ExplanationFor divisibility by 4, the last two digits must form a number divisible by 4. With x = 0, the last two digits are 40, and 40 ÷ 4 = 10. So x = 0 works and is the smallest option listed.
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DS1 Medium
Is the positive integer N divisible by 12?
Statement IN is divisible by 4.
Statement IIN is divisible by 3.
ExplanationDivisibility by 12 requires both 4 and 3 (since gcd(4,3)=1). Statement I alone allows N = 8 (not divisible by 3). Statement II alone allows N = 6 (not divisible by 4). Together, N must be divisible by lcm(4,3) = 12. -
DS2 Easy
Is the integer x divisible by 6?
Statement Ix is divisible by 2.
Statement IIx is divisible by 3.
ExplanationA number is divisible by 6 only when it is divisible by both 2 and 3. Each statement alone is insufficient (e.g. 4 is divisible by 2 but not 6; 9 is divisible by 3 but not 6). Both together guarantee divisibility by 6.
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DS3 Medium
What is the remainder when N is divided by 9?
Statement IThe sum of the digits of N is 27.
Statement IIN is a three-digit number less than 500.
ExplanationIf the digit sum is 27, the remainder on division by 9 is 27 mod 9 = 0. Statement I alone fixes the remainder. Statement II only restricts the size of N and does not fix the remainder. -
DS4 Hard
Is the five-digit number 63a5b divisible by 35?
Statement Ia + b = 8.
Statement IIb = 3.
ExplanationA number divisible by 35 must end in 0 or 5 (divisible by 5). Statement II gives b = 3, so the number cannot be divisible by 5 — hence not divisible by 35. That is enough to answer the question (No). Statement I alone does not fix b to 0 or 5.